The objectives are (1) new or improved quantitative methods of assessing the health effects of exposures to combinations of environmental toxicants, especially carcinogens; (2) application of these methods to data from human studies and animal experiments. The methods include (a) use of quantitative models (e.g. the multi-stage theory of cancer induction and its extensions) to suggest relevant parameters and summary statistics; (b) the development of statistical criteria for determining when data can be pooled over extraneous variables without introducing bias for relationships of interest.